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Sunday, July 27, 2008

Replacement Resistance

Here is a little problem from the physical/electro-technical area. Only basic knowledge about electricity and resistance is required, like:

* The replacement resistance of two serial connected resistances

is 2 Ohm (Rreplacement = R1 + R2, where R1 = R2 = 1).

* The replacement resistance of two parallel connected resistances

is 1/2 Ohm (1/Rreplacement = 1/R1 + 1/R2, where R1 = R2 = 1).

The Question: What is the replacement resistance of the circuit below?

A Hint: The solution is rather easy and lies in the range of [0..5].

Answer: The circuit can be redrawn as follows:

The voltage at both ends of the middle resistance is now equal and therefore the circuit consists of two parallel parts, each consisting of two serial resistances.

Conclusion: The replacement resistance Rreplacement is 1 (1/Rreplacement = 1/(1+1) + 1/(1+1)).

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